For CSA Research , we had been given a selection form where we had to fill our choices of the research area, sub areas and background subjects which we wanted to be interviewed on. My choice-

Research area - Intelligentsystems

Sub areas - Machinelearning, datamining

Background subjects - Probability, LinearAlgebra

Before the interview, we had a short half an hour written test. The paper for written test was different for every research area group - Intelligent Systems, Theoretical Computer Science and Computer systems.

The test was moderately easy with 10 questions in total. It had 2 questions from probability, 2 questions from eigen values and characteristic equation of a matrix, 1 question to sort the given functions into increasing order of time complexity, 1 question to guess the output of a c program, 1 question from computer organization cache part(to calculate the no of bits in tag field). There were 3 more questions which I don't remember.

My advice on written test- In the question paper itself we had rough work area below each question. Try to provide the solution of your answer neatly in that area for each question as well. This might help the interviewers to know your level of understanding. Moreover it might create a good impression of you on them.

I could answer 7/10 questions and all were correct to my knowledge. The results of the test was quickly announced within 1 hour. I was shortlisted and we were headed towards our interview rooms. My interview panel had 3 professors.

I1: Suman, you have graduated from IIEST Shibpur in 2015 and you have a cgpa of 8.02.

Me: Yes sir.

I1: So what did you do for these 2-3 years after graduation?

Me: Sir, I was working at Lexmark International India Pvt. Ltd as a software engineer mainly on automation.(They did not seem much interested in knowing my job profile though).

I1: So Suman, you have selected Intelligent systems as your reasearch area and selected mc learning and data mining as sub area with background subjects probability theory and linear algebra?

Me: Yes sir.

I1: So what are the topics you have prepared for linear algebra?

Me: Matrices and determinants, Eigen values.

I1: Shall we start with eigen values?

Me: Yes sir.

I1: What are eigen values and eigen vectors?

Me: Answered.

I1: If you are given a matrix of order mxn, what are the number of eigen values it will have and why?

Me: (There was a trick in this question) Sir, for a matrix A to have eigen values we should have the order of A as nxn(i.e. it should be a square matrix and determinants exists only for square matrix). When we write the characteristic equation of the matrix, it comes out be a polynomial equation of degree n, and no of roots of a polynomial equation of degree n is n. The roots of this equation will be the eigen values, hence n eigen values for an nxn matrix.

I1: What do you mean by degree of a polynomial?(At this point I understood that they dig really deep to know whether we understand the basic maths concepts or not)

Me: The highest power of x in a polynomial in terms of x.

I1: Can a matrix of order 3 have 3 eigen values, two of them real and one of them complex?

Me: No sir. Because the characteristic equation of this matrix will be a polynomial of degree n and every polynomial equation has complex roots, if any in conjugate pairs. (This was a tough question for me and I gave a wrong answer).

I1: Take an example of a diagonal matrix and write it on the board.(I wrote). The matrix looked somewhat like this -

I1: Looking at this example can you say that it is possible to have a complex eigen value and two real eigen values?

Me: (Confused) Yes sir. (Clearly it can be seen that eigen values of this matrix are 3i,1 and 2. So I said yes. But I am still confused about this.)

I1: Lets proceed further. Given a matrix relation A2=A, can u determine what will be the value of rank(A)+ rank(A-I)?

Me:(I was completely unaware of this, still I tried to deduce something.) It can be seen that A is an idempotent matrix. With the given relation we can write-

A(A-I)=0, which means either A=0 or A=I (which is completely wrong. By now they would have seriously started doubting me.)

I1: Okay lets proceed Suman.

Me: (I somehow remembered for the previous question that if product of 2 matrices AB=0, it is not necessary that either A or B has to be a null matrix. I quickly fixed my mistake by saying it.) Sir, I made a mistake there, it is not necessary that either one of A and A-I has to be zero.

I1: Okay.

After this I was handed over to the 2nd professor who remained quiet all this while.

I2: What are the topics you have prepared in probability?

Me: Sir conditional probability, random variables.

I2: Okay so do you know what is a CDF?

Me: No Sir.

I2: (surprised) Have you never heard of it?

Me: (At that moment I could not remember anything as I was disappointed with my performance so far) No Sir. But I know what a PDF is.

I2: What is a PDF?

Me: Sir probability density function(I could have also said probability distribution function but this is what I could remember at that time. I explained what a probability density function in detail by explaining it on board with the help of graph of a random pdf. I also explained how the integration of probabilities of all the points on x axis turns out to be 1.)

I2: Okay. Can you tell what is the pdf of an exponential random variable?

Me: (My confidence went down further because I remembered the pdfs for all other random variables except this. I still said yes in the heat of the moment)Yes sir. It is

I2: Okay. Prove how the sum of probabilities for all the points for this random variable is equal to 1.

Me: I tried by integrating this function over x from x=0 to 1.(Even though my function was incorrect I tried to follow the correct method of proving it. The interviewers helped me one or two times wherever I was stuck, still my result was not coming out to be 1 because of the incorrect function I was using. I even remembered and said the correct function for exponential random variable somewhere in the between, but the interviewer said that the function does not matter, which implied that he was more interested in the approach I was following)

Written tests and interviews were conducted over a period of 5 days(21st may to 25th may). On each day there were 2 slots(morning and afternoon) and mine was in the morning slot. In my slot, there were around 20 candidates who came in for intelligent systems and around 15 candidates in systems and theoretical computer science each for the written test and interview. In the written test all the candidates from intelligent systems were shortlisted for the interview. I think the shortlisting for the interview from the written test is based on the cutoff set i.e. the number of questions answered in the written test. If all the candidates meet the cut off, everyone will be shortlisted for the interview. I also remember someone saying that on the same day in the afternoon slot, none of the candidates appearing for intelligent systems test was shortlisted for the interview.